Writing slope-intercept equations
Click here ?? to get an answer to your question ?? The linear equation when b = 5 and m = –2 is y = 5x – 2. y = 5x + 2. y = –2x – 5. y = –2x + 5.and watch and you
Writing the Equation of a Line. Learning Objective s. A linear equation can be expressed in the form. In this equation, x and y are coordinates of a point, m is the slope , and b is the y -coordinate of the y-intercept. Because this equation describes a line in terms of its slope and its y -intercept, this equation is called the slope-intercept form. When working with linear relationships, the slope-intercept form helps to translate between the graph of a line and the equation of a line.
There are other ways to write the linear equation of a straight line than the slope-intersect form previously described. We've got a line with the slope 2. One of the points that the line passes through has got the coordinates 3, 5. It's possible to write an equation relating x and y using the slope formula with. Since we used the coordinates of one known point and the slope to write this form of equation it is called the point-slop form. Since the slope of a vertical line is undefined you can't write the equation of a vertical line using neither the slope-intersect form or the point-slope form. But you can express it using the standard form.
Linear equations equations whose graphs are a line can be written in multiple formats, but the standard form of a linear equation looks like this:. A , B and C can be any number--including negative numbers, zero and one! So examples of standard form can look like this:. Notice that in this case, B is negative five! Standard form is great for finding the x and y intercepts of a graph, that is, the point where the graph crosses the x -axis and the point where it crosses the y -axis.
Caroline is a full-time college student planning a spring break vacation. She arranged for direct deposit of her payroll checks. If she can only work 4 hours per day, how many days per week will she have to work? How many weeks will it take? In this section, we will investigate problems like this and others, which generate graphs like the line in Figure.
Linear Equations A linear equation looks like any other equation. It is made up of two expressions set equal to each other. A linear equation is special because: It has one or two variables. No variable in a linear equation is raised to a power greater than 1 or used as the denominator of a fraction. When you find pairs of values that make the linear equation true and plot those pairs on a coordinate grid, all of the points for any one equation lie on the same line. Linear equations graph as straight lines. A linear equation in two variables describes a relationship in which the value of one of the variables depends on the value of the other variable.
Graphing a Linear Equation
In the slope-intercept form you use the slope of the line and the y-intercept to express the linear function., Many students find this useful because of its simplicity.
Given the algebraic equation of a line, we are able to graph it in a number of ways. In this section, we will be given a geometric description of a line and be asked to find the algebraic equation.,